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    1-115-ModelingWithFirstOrderODEs-ModelingScenario
    Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.

    Keywords: bacteriafalling objectNewton's Law of Coolingdrugcoolingdrag

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    1-140-LeakyBucket-ModelingScenario
    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top...

    Keywords: flowTorricelli's Lawleaky bucket

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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen...

    Keywords: Probabilitystochastic processesBayesian methodsprobability distribution

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    1-142-WaterBottles-ModelingScenario
    This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or...

    Keywords: data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle

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    3-060-DataToDifferentialEquation-ModelingScenario
    Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.

    Keywords: Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of...

    Keywords: Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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    1-036-NeutralBuoyancy-ModelingScenario
    An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon

    Keywords: DensitybuoyancyArchimedes’ Principlefloatneutral buoyance

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    1-004-MicroorganismImmigration-ModelingScenario
    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

    Keywords: continuousimmigrationpopulationdeathdiscrete

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    6-009-FakeNews-ModelingScenario
    In modern society, creating and disseminating information is easier than ever. In this project, you will model the spread of fake news and investigate ways to deter distributing misinformation.

    Keywords: sensitivity analysisSIR modelsSIS modelfake news

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    6-028-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.

    Keywords: concentrationcomparmentsalttankmixing

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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the...

    Keywords: driversteady statesum of square errors

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    3-150-ItsABlastFurnace-ModelingScenario
    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.

    Keywords: steady stateheat equationinverse problemfurnace

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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.

    Keywords: Polynomial dynamical systembeamcantilever

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    5-002-RelationshipDynamics-ModelingScenario
    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.

    Keywords: love affairRomeo and Juliet

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

    Keywords: Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency

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    4-055-ShatterWineGlass-ModelingScenario
    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?

    Keywords: frequencydampingamplituderesonanceoscillationshatteringwine glassbridgesaircraftexternal force

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    3-095-ShotInWater-ModelingScenario
    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.

    Keywords: projectile motionterminal velocityprojectilewater resistancereduction of orderfrictionair resistance

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    3-105-FrequencyResponse-ModelingScenario
    We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.

    Keywords: transient dynamicscircuitspring massdriverfrequency responseamplitudesteady state

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    3-044-DeepWell-ModelingScenario
    We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.

    Keywords: gravityprojectile motionfalling bodyspeed of sound

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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more...

    Keywords: diseasecommon coldresidence hall

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